Unit 4 Dynamics I: Inertia and Interactions of Particles

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You've heard the story before. Someone is sitting in their car at a stop light, minding their own business, and CRACK!!#**!!!#*!, someone "rear ends" them. Usually for a week or so afterwards, the driver and passenger who were in the car that got hit complain of whiplash.

If you ask them what whiplash is, they'll likely tell you it's when their head gets thrown backwards. If you really think about it, is their head really getting thrown back? If you were an observer outside of the car, you would see their bodies propelled forward when the car is hit, while their heads were actually staying in the same place. This is just one of many examples of the first law of motion proposed first by Galileo and later by Isaac Newton. Simply put, the law of inertia (usually called Newton's 1st law):

  • A body at rest will tend to stay at rest unless an unbalanced force acts upon it. Likewise, a body in motion will continue in its motion in a straight line unless it is acted upon by an unbalanced force.

You feel the effects of inertia whenever you turn a corner in your car. Your car turns left and you feel like your being pulled to the right. Actually your body wants to go straight but you perceive it as being pulled to the right. Maybe you're driving down the road and a deer runs in front of your car. You put the brakes on and your car slows down and you feel pushed forwards. Actually, your body wants to continue traveling at the velocity you were traveling at immediately before you put on your brakes.

Force Diagrams

Of course, if there is an unbalanced force acting on an object, it will not stay at rest or a constant velocity. In nearly all cases, multiple forces act on an object. In order to resolve a complex situation involving multiple forces, we need to represent them using force diagrams. Any force acting on an object, be it a push or pull can be represented by an arrow acting in the direction of the force. In all diagrams, the tail of the arrow is at the center of the object. The following diagrams represents a push or pull to the left. The size of the arrow is proportionate to the magnitude of the force. In this case, F1 > F2.


Below is a diagram of the forces acting on a box sitting on the table. Notice the gravitational force (the object's weight) is balanced out by the normal force exerted by the table on the box.

Components of Forces

It is useful to consider an object in the context of a coordinate system. For example, in the above diagram, the table top is parallel to the x-axis and both gravity and normal forces act parallel to the y-axis. Of course, many forces aren't as cooperative to act along the x or y-axis. Many act at an angle. These forces can be resolved into components by considering the actual force the hypoteneuse of a right triangle. This force can be resolved into x and y components by just drawing in the legs of the triangle so that they lie on each axis. It might be helpful at first to draw 2 right triangles, one above and one below the hypoteneuse. The components that "act" on the object have the arrows.


Remember, the components are equivalent to the force acting on the object. They replace it.

Calculating the Force of Gravity

If a plot of weight (Fg) vs. mass is made, the result is a straight line with a slope of 9.8 N/kg. The mathematical model that relates weight and mass is:

Fg = mg

Interactions Between Objects

Objects interact through several ways. The sun and earth interact by gravitational force. The proton and neutron interact through static electrical forces. The magnet at the earth's pole and your compass interact with each other. When a batter hits a baseball, he or she can feel it.

These are all examples of Newton's third law of motion (yeah, I know, we missed the second). Newton's third law states:

  • When two objects interact the exert equal but opposite forces on each other.

Beware! This law seems deceptively simple, yet most physics students miss the boat. Let's look at some examples.

  • The earth pulls down on a person with a force Fe,p. The person pulls up on the earth with a force of Fp,e.
  • You push on the wall with a force of Fp,w. The wall pushes back on you with a force of Fw,p.
  • A proton attracts an electron with a force of Fp,e. The electron attracts the proton with a force Fe,p.

Notice the equal and opposite forces act on different objects. One force would be designated positive and the other would be negative since it acts in the opposite direction.

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